Question

The position of an object in simple harmonic motion is defined by the function y = (0.50 m) sin (πt/2). Determine the maximum speed of the object.

Answer 1

The maximum speed of the object under simple harmonic motion is 0.786 m/s.

The given parameters:

• Position of the particle, y = 0.5m sin(πt/2)

Wave equation for simple harmonic motion;

y = A sin(ωt + Ф)

where;

• A is the amplitude = 0.5 m
• ω is the angular speed = π/2

The maximum speed of the object is calculated as follows;

$V_{max} = A \omega\\\\V_{max} = 0.5 \times \frac{\pi}{2} = \frac{\pi}{4} \ m/s = 0.786 \ m/s$

Thus, the maximum speed of the object under simple harmonic motion is 0.786 m/s.

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